Solve 1/4/I=1/3+frac{1/4}{frac{2}{3}+frac{2}{3}}=

$$\frac { \frac { 1 } { 4 } } { I } = \frac { \frac { 1 } { 3 } + \frac { 1 } { 4 } } { \frac { 2 } { 3 } + \frac { 2 } { 3 } } =$$

Solve for I

$$I=\frac{4}{7}\approx 0.571428571$$

Steps for Solving Linear Equation

Variable I cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by I.

$$\frac{1}{4}=\frac{3}{4}I\left(\frac{1}{3}+\frac{1}{4}\right)$$

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{1}{4}=\frac{3}{4}I\left(\frac{4}{12}+\frac{3}{12}\right)$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{1}{4}=\frac{3}{4}I\times \frac{4+3}{12}$$

Add 4 and 3 to get 7.

$$\frac{1}{4}=\frac{3}{4}I\times \frac{7}{12}$$

Multiply \frac{3}{4} times \frac{7}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{4}=\frac{3\times 7}{4\times 12}I$$

Do the multiplications in the fraction \frac{3\times 7}{4\times 12}.

$$\frac{1}{4}=\frac{21}{48}I$$

Reduce the fraction \frac{21}{48} to lowest terms by extracting and canceling out 3.

$$\frac{1}{4}=\frac{7}{16}I$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{7}{16}I=\frac{1}{4}$$

Multiply both sides by \frac{16}{7}, the reciprocal of \frac{7}{16}.

$$I=\frac{1}{4}\times \frac{16}{7}$$

Multiply \frac{1}{4} times \frac{16}{7} by multiplying numerator times numerator and denominator times denominator.

$$I=\frac{1\times 16}{4\times 7}$$

Do the multiplications in the fraction \frac{1\times 16}{4\times 7}.

$$I=\frac{16}{28}$$

Reduce the fraction \frac{16}{28} to lowest terms by extracting and canceling out 4.

$$I=\frac{4}{7}$$